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United States Patent |
5,324,939
|
Louris
,   et al.
|
June 28, 1994
|
Method and apparatus for ejecting unwanted ions in an ion trap mass
spectrometer
Abstract
A method and apparatus is described which determines a plurality of spaced
discrete frequencies covering the range of frequencies of the
characteristic motion of unwanted ions and processes said discrete
frequencies to generate a plurality of time dependent voltage amplitude
values which vary throughout the time domain such that the frequency
content of said plurality of time dependent voltage amplitude values is
relatively uniform over the entire time domain, and such that the
magnitude associated with the discrete frequencies is relatively uniform
over the frequency domain.
Inventors:
|
Louris; John N. (Santa Clara County, CA);
Taylor; Dennis M. (Santa Clara County, CA)
|
Assignee:
|
Finnigan Corporation (San Jose, CA)
|
Appl. No.:
|
068915 |
Filed:
|
May 28, 1993 |
Current U.S. Class: |
250/292; 250/291 |
Intern'l Class: |
H01J 049/42 |
Field of Search: |
250/292,291,282
|
References Cited
U.S. Patent Documents
4761545 | Aug., 1988 | Marshall et al. | 250/291.
|
4818869 | Apr., 1989 | Weber-Grabau | 250/282.
|
4945234 | Jul., 1990 | Goodman et al. | 250/291.
|
5013912 | May., 1991 | Guan et al. | 250/282.
|
5107109 | Apr., 1992 | Stafford, Jr. et al. | 250/282.
|
5134286 | Jul., 1992 | Kelley | 250/282.
|
5248882 | Sep., 1993 | Liang | 250/291.
|
Foreign Patent Documents |
0362432 | Apr., 1990 | EP.
| |
Primary Examiner: Berman; Jack I.
Attorney, Agent or Firm: Flehr, Hohbach, Test, Albritton & Herbert
Claims
What is claimed:
1. An ion trap mass spectrometer apparatus comprising:
an ion trap having a plurality of electrodes,
means for establishing ion trapping fields within said ion trap for
trapping ions over a predetermined mass range,
ion excitation means for resonantly ejecting ions trapped in said ion trap
including:
means for determining a plurality of spaced discrete frequencies covering
the range of frequencies of the characteristic motion of ions which are to
be resonantly ejected from the ion trap,
means for processing said discrete frequencies to generate a plurality of
time dependent voltage amplitude values which vary throughout the time
domain such that the frequency content of said time dependent voltage
amplitude values is relatively uniform over the entire time domain, and
such that the magnitude of the discrete frequencies is relatively uniform
over the frequency domain, and
means for applying said time dependent voltage amplitude values to said ion
trap electrodes whereby to resonantly eject said ions.
2. An ion trap mass spectrometer apparatus as in claim 1 wherein said
frequencies are equally spaced.
3. An ion trap mass spectrometer apparatus as in claim 1 wherein said
frequencies are unequally spaced.
4. An ion trap mass spectrometer apparatus as in claim 1 wherein said
plurality of spaced discrete frequencies have phases such that the
frequency components are not in phase at any one point.
5. An ion trap mass spectrometer apparatus as in claim 4 wherein said
phases are varied non-linearly with frequency.
6. An ion trap mass spectrometer apparatus as in claim 4 wherein said
phases are varied quadratically with frequency.
7. An ion trap mass spectrometer apparatus as in claim 1 wherein one or
more of said discrete frequencies are removed from said range of
frequencies of the characteristic motion of ions whereby ions having
characteristic motion at said frequencies are not resonantly ejected.
8. An ion trap mass spectrometer apparatus as in claim 1 wherein one or
more of said discrete frequencies are removed from said plurality of time
dependent voltage amplitude values whereby ions have corresponding
characteristic frequencies of motion are not resonantly ejected.
9. An ion trap mass spectrometer apparatus as in claim 1 wherein said
plurality of spaced discrete frequencies cover two or more separated
ranges of frequencies corresponding to the characteristic frequencies of
motion of two or more discrete m/z ranges of ions to be resonantly
ejected, and being separated by frequency gaps or notches which correspond
to the characteristic frequencies of motion of ions which are not to be
resonantly ejected, but are to be accumulated within said apparatus.
10. A method for resonantly ejecting ions stored in an ion trap comprising
the steps of
determining a plurality of spaced discrete frequencies covering the range
of frequencies of characteristic motion of the ions which are to be
resonantly ejected,
processing said discrete frequencies to generate a plurality of time
dependent voltage amplitude values which vary throughout the time domain
such that the frequency content of said time dependent voltage amplitude
values is relatively uniform over the entire time domain, and such that
the magnitude of the discrete frequencies is relatively uniform over the
frequency domain, and
applying said time dependent voltage amplitude values to said ion trap
electrodes whereby to resonantly eject said ions.
11. A method for resonantly ejecting ions from an ion trap as in claim 10
wherein one or more of said discrete frequencies are removed from said
range of frequencies of the characteristic motion of ions, whereby ions
having characteristic motion at said frequencies are not ejected.
12. A method for resonantly ejecting ions from an ion trap as in claim 10
wherein one or more of said discrete frequencies are removed from said
plurality of time dependent voltage amplitude values whereby ions having
corresponding characteristic frequencies of motion are not ejected.
13. A method for resonantly ejecting ions from an ion trap as in claim 10
wherein said plurality of spaced discrete frequencies cover two or more
separated ranges of frequencies corresponding to the characteristic
frequencies of motion of two or more discrete m/z ranges of ions to be
resonantly ejected, and being separated by frequency gaps or notches which
correspond to the characteristic frequencies of motion of ions which are
not to be resonantly ejected, but are to be accumulated within the ion
trap.
14. A method for resonantly ejecting ions stored in the ion trap of a mass
spectrometer which stores ions over a predetermined mass range including
the steps of:
determining a series of spaced sine functions which have phases that vary
non-linearly with frequency, said sine functions covering the range of
frequencies of the characteristic motion of ions to be ejected,
summing the series of sine functions to provide a waveform which has a
series of closely spaced discretely separated peaks in the frequency
domain, such that the difference in ejection efficiency between an ion
having a characteristic frequency of motion which coincides with a
discrete frequency component of the waveform, and an ion having a
characteristic frequency of motion which falls between the discrete
frequency components of the waveform is small, and
applying said waveform to the ion trap to resonantly eject selected ions.
15. A method for resonantly ejecting ions stored in an ion trap including
the steps of:
determining a series of spaced sine functions which have phases that vary
non-linearly with frequency, said sine functions covering the range of
frequencies of the characteristic motion of ions to be ejected,
summing the series of sine functions to provide a waveform which has a
series of spaced discretely separated peaks in the frequency domain, such
that the difference in frequencies between successive discretely separated
peaks in the frequency domain is at least four times the reciprocal of the
time interval over which the waveform is to be applied, and
applying said waveform to the ion trap to resonantly eject selected ions.
16. A method for resonantly ejecting ions stored in an ion trap including
the steps of:
determining a series of spaced sine functions which have phases that vary
non-linearly with frequency, said sine functions covering the range of
frequencies of the characteristic motion of ions to be ejected,
summing the series of sine functions to provide a waveform which has a
series of spaced discretely separated peaks in the frequency domain, such
that the difference in frequencies between successive discretely separated
peaks in the frequency domain is at least two times the reciprocal of the
time interval over which the waveform is to be applied, and
applying said waveform to the ion trap to resonantly eject selected ions.
17. The method of claim 15 wherein before applying said waveform to the ion
trap the waveform is subjected to a digital filter to alter the frequency
spectrum of the waveform.
18. The method of claim 16 wherein before applying said waveform to the ion
trap the waveform is subjected to a digital filter to alter the frequency
spectrum of the waveform.
19. The method of claim 15 wherein the waveform is subjected to an analog
filter at the time of applying said waveform to the ion trap to alter the
frequency spectrum of the waveform.
20. The method of claim 16 wherein the waveform is subjected to an analog
filter at the time of applying said waveform to the ion trap to alter the
frequency spectrum of the waveform.
21. A method for resonantly ejecting ions stored in an ion trap including
the steps of:
calculating a waveform in which the magnitude part of the frequency
spectrum is assigned in such a way that the frequency spectrum
substantially consists of a series of discretely separated peaks covering
a range of frequencies corresponding to the characteristic frequencies of
ions to be ejected and in which the phase part of the frequency spectrum
is assigned as a nonlinear function of frequency and in which the time
domain waveform is calculated by application of the inverse Fourier
transform, and
applying said waveform to the ion trap to resonantly eject selected ions.
22. A method for resonantly ejecting ions stored in an ion trap including
the steps of:
calculating a waveform in which the magnitude part of the frequency
spectrum is assigned in such a way that the frequency spectrum
substantially consists of a series of discretely separated peaks covering
a range of frequencies corresponding to the characteristic frequencies of
ions to be ejected and such that the difference in frequencies between the
successive peaks in the frequency domain is at least four times the
reciprocal of the time interval over which the waveform is to be applied,
and in which the phase part of the frequency spectrum is assigned as a
nonlinear function of frequency and in which the time domain waveform is
calculated by application of the inverse Fourier transform, and
applying said waveform to the ion trap to resonantly eject selected ions.
23. A method for resonantly ejecting ions stored in an ion trap including
the steps of:
calculating a waveform in which the magnitude part of the frequency
spectrum is assigned in such a way that the frequency spectrum
substantially consists of a series of discretely separated peaks covering
a range of frequencies corresponding to the characteristic frequencies of
ions to be ejected and such that the difference in frequencies between the
successive peaks in the frequency domain is at least two times the
reciprocal of the time interval over which the waveform is to be applied,
and in which the phase part of the frequency spectrum is assigned as a
nonlinear function of frequency and in which the time domain waveform is
calculated by application of the inverse Fourier transform, and
applying said waveform to the ion trap to resonantly eject selected ions.
24. A method for resonantly ejecting ions stored in an ion trap including
the steps of:
calculating a waveform in which the magnitude part of the frequency
spectrum is substantially a series of discretely separated peaks covering
a range of frequencies corresponding to the characteristic frequencies of
ions to be ejected, and
applying said waveform to the ion trap to resonantly eject selected ions.
25. A method for resonantly ejecting ions stored in an ion trap including
the steps of:
calculating a waveform in which the magnitude part of the frequency
spectrum substantially consists of a series of discretely separated peaks
covering a range of frequencies corresponding to the characteristic
frequencies of ions to be ejected and such that the difference in
frequencies between the successive peaks in the frequency domain is at
least four times the reciprocal of the time interval over which the
waveform is to be applied, and p1 applying said waveform to the ion trap
to resonantly eject selected ions.
26. A method for resonantly ejecting ions stored in an ion trap including
the steps of:
calculating a waveform in which the magnitude part of the frequency
spectrum substantially consists of a series of discretely separated peaks
covering a range of frequencies corresponding to the characteristic
frequencies of ions to be ejected and such that the difference in
frequencies between the successive peaks in the frequency domain is at
least two times the reciprocal of the time interval over which the
waveform is to be applied, and
applying said waveform to the ion trap to resonantly eject selected ions.
Description
BRIEF DESCRIPTION OF THE INVENTION
This invention relates to a method and apparatus for ejecting the ions in
an ion trap mass spectrometer.
BACKGROUND OF THE INVENTION
Mass spectrometers are used to determine the chemical identity of
substances by determining the mass of ions derived from the substances.
The mass of an ion is determined by using the known behavior of charged
particles in electric and magnetic fields, with some characteristic of the
ion trajectory being observed and used to deduce the mass-to-charge ratio
of the ion. Mass spectrometers may be divided into two broad classes:
instruments that produce a beam of ions to effect mass analysis (such as
magnetic sector spectrometers and quadrupole spectrometers) and
instruments that trap a population of ions to effect mass analysis (such
as ion cyclotron resonance mass spectrometers and Paul ion trap mass
spectrometers).
The various types of mass spectrometers have advantages and disadvantages,
and a large variety of instruments are now commercially available. No one
type of instrument can deliver the necessary performance in all types of
applications at an acceptable cost, and vigorous competition exists
between the manufacturers of the various types of instruments to increase
performance while controlling cost.
One disadvantage of trap-type mass spectrometers, either the Paul ion trap
mass spectrometer or the ion cyclotron resonance mass spectrometer (ICR),
is that the presence of the population of ions necessarily perturbs the
electric field experienced by the ions, so that the ion trajectories
depend on the number of ions present. This results in inaccuracy in the
determination of m/z, because the field perturbation is quite complex, and
the number of ions may change during mass analysis. The "space charge"
introduced by the ions limits the number of ions that may be present
during mass analysis if mass accuracy (and mass resolution) are to be
maintained. For the Paul ion trap mass spectrometer, the practical effect
of space charge is that the dynamic range (for purposes of mass analysis)
is limited to about two orders of magnitude, because the more abundant
ions "fill" the trap before the population of non-abundant ions is great
enough to be detected with an adequate signal-to-noise ratio.
This limitation is most severe in those applications where the amount of
analyte varies widely and unpredictably, such as in the gas
chromatographic/mass spectrometric investigation of samples encountered in
environmental analysis. Because of the costly high-field electromagnets
needed for ion cyclotron resonance spectrometers, these instruments have
seen little commercial use as detectors in chromatographic instruments for
which the detector must be relatively inexpensive. In contrast, Paul ion
trap mass spectrometers are now used almost exclusively as GC detectors,
so the space charge limitation to dynamic range, although important to
both types of spectrometer, is of more practical importance in Paul ion
trap mass spectrometers.
An important development in the use of the Paul ion trap as a
chromatographic detector was the dynamic control of the number of ions
stored in the trap by adjusting the length of time during which ions are
formed. U.S. Pat. No. 5,107,109 describes a method wherein a preliminary
analysis is performed to estimate the rate of ion formation, and the
actual mass analysis is then accomplished by using an ionization interval
(calculated from the rate of ion formation) that gives a fixed, "target"
number of ions in the trap. For well-separated chromatographic peaks, this
dynamic control of the ionization time can extend the dynamic range so
that analytes of concentrations varying by as much as five orders of
magnitude can be successfully mass-analyzed. However, if the compounds are
not chromatographically resolved, dynamic control of the ionization time
will allow the acquisition of the mass spectrum of the mixture of the two
compounds, but the internal dynamic range of the mass spectrum is limited
to two orders of magnitude, and the less abundant compound may not be
observed at all.
Another method of controlling the extent of space charge is the selective
exclusion of ions from the trap, either during or after the formation of
ions. From the time of the first commercial introduction of the Paul ion
trap mass spectrometer, the r.f. voltage during ionization was adjusted so
that certain low-mass ions (from air, water, etc.) would not be stored
during ionization. Dawson and coworkers used a combined DC and r.f. field
during ionization that allowed only a narrow mass range to be stored.
March and coworkers (M. A. Armitage, J. E. Fulford, D. -N. Hoa, R. J.
Hughes and R. E. March, "The Application of Resonant Ion Ejection to
Quadrupole Ion Storage Mass Spectrometry: A Study of Ion/Molecule
Reactions in the QUISTOR," 1979, Can. J. Chem., vol. 57, pp. 2108-2113)
used resonance ejection to selectively eliminate ions from the trap. Use
of alternating steps of ionization and ejection of undesired ions through
the use of a DC field is described by Weber-Grabau (U.S. Pat. No.
4,818,869). Franzen et al. (European patent application, publication
0362432) describe the use of broadband waveforms for the resonance
ejection of undesired ions during ionization.
The use of broadband waveforms for the ejection of ions from the ion
cyclotron resonance trap is well established, although this has mostly
been done for purposes other than simply controlling space charge, such as
ion isolation prior to an ms/ms experiment. The early workers used noise
waveforms (generated by analog methods) for ion ejection, but Marshall et
al. (U.S. Pat. No. 4,761,545) describe calculated waveforms tailored to
the particular experiment. In Marshall et al., a table of numbers is
stored in a digital memory and these points are sequentially converted to
an analog voltage by a digital-to-analog converter and associated
electronic circuits. The "arbitrary waveform" was calculated by Marshall
et al. by first choosing the desired frequency spectrum of the waveform
and then using the inverse Fourier transform to calculate the waveform
having the desired frequency spectrum. This technique of calculating a
waveform using the inverse Fourier transform (inverse FT or FFT for "fast
Fourier transform") and then creating the waveform by successively
converting to analog form the digital values in a stored table is called
the SWIFT method (for Stored Waveform Inverse Fourier Transform).
Formally, the Fourier transform maps a complex function to a complex
function. Practically, a waveform is a pure real function (amplitude as a
function of time) which is called the "time domain", and the Fourier
transform maps this to a complex function (a complex quantity as a
function of frequency) which is called the "frequency domain". The inverse
Fourier transform maps the complex function to the time domain and the
discrete inverse Fourier transform (used for numerical computation) acts
on an array of complex data. Each point in the array may be described
using the cartesian representation (with a real and an imaginary part) or
equivalently by using the polar representation (with a magnitude and a
phase part), but algorithms for calculating the forward and inverse
discrete Fourier transform generally use the cartesian representation. The
polar representation has the advantage that the magnitude and phase parts
are closely related to the familiar parameters of simple cosine waves: the
magnitude part of the frequency spectrum at a particular frequency
corresponds to the amplitude of the cosine function associated with that
frequency, and the phase part of the frequency spectrum at that frequency
corresponds to the phase of the cosine function. For a particular
application of Marshall's method, the magnitude part of the frequency
spectrum is assigned according to the efficiency with which ions are to be
ejected; in a typical application the magnitude would be a constant for
those frequencies associated with ions that are to be ejected, the
magnitude would be zero for some range of frequencies associated with ions
that are to be retained within the cell, and the magnitude would likewise
be zero for frequencies outside the range of possible ion frequencies.
The phase part of the frequency spectrum is more difficult to assign,
because there is no single, simple criterion that unambiguously leads to a
phase assignment. For a given assignment of the magnitude part of the
frequency spectrum, each possible assignment of the phase part of the
frequency spectrum governs the time course of the resulting time domain
waveform that results from the inverse Fourier transform. Marshall et al.
noted that for the simple, useful magnitude assignment in which the
magnitude is everywhere zero, except for a range of frequencies at which
it is constant, the simplest conceivable phase assignment of zero at all
frequencies results in a time domain waveform that is essentially a very
narrow pulse. These workers rejected this phase assignment because the
high amplitude during the pulse results in the need for excessive dynamic
range in both the analog and digital parts of the electronic hardware
needed to produce the waveform. They recommended the assignment of the
phase as a quadratic function of the frequency; the resulting time domain
waveform is not pulse-like, but has the power distributed throughout the
time period so that the dynamic range requirements of the electronics are
much less demanding. More recently, Goodman et al. (U.S. Pat. No.
4,945,234) and Guan et al. (U.S. Pat. No. 5,013,912) have further
developed methods for assigning the phase part of the frequency spectrum.
That the ion motions in ICR traps and Paul traps share enough
characteristics that the waveforms used for ion ejection are much the same
in both instruments has been recognized since the work of Marshall et al.,
who described the SWIFT technique for both traps. In the ICR trap the ion
trajectories are circular, but the excitation voltage is applied between
opposing plates and the motion in the coordinate normal to the plates is
sinusoidal, with the frequency of the motion being inversely proportional
to the m/z of the ion. In the Paul trap, the excitation voltage is applied
between the two end cap electrodes, while the ion motion is a
reciprocating motion between the two electrodes. Over a large range of
useful operating conditions the reciprocating motion may be approximated
as being sinusoidal, with a frequency that is inversely proportional to
the m/z of the ion. For both traps (within the limits of this
approximation), the response of the ions to an excitation voltage is
described by the linear, inhomogeneous differential equation commonly
described as the equation of forced harmonic motion. Thus, much the same
waveforms may be used in both Paul traps and ICR traps, and theoretical as
well as practical considerations are shared in the development of
waveforms for the two types of instrument. Guan and Marshall have
described in some detail the relationship between the theories of ion
ejection in the Paul trap and the ICR trap (Anal. Chem. 65, 1288-1294
(1993)).
Recently Kelley described the use of noise waveforms for the isolation of
ions of a narrow mass range in the Paul ion trap (U.S. Pat. No.
5,134,286). He described the application of a frequency band-reject filter
to a noise waveform so that the resulting waveform would cause all ions
with resonant frequencies other than those within a specified band to be
ejected from the trap. Kelley did not specify whether the noise waveform
was created with an analog noise generator or with a digital arbitrary
waveform generator.
When attempting to apply the previously described methods (e.g. the methods
of Marshall, Franzen and Kelley) to the problem of selectively ejecting
ions during the ionization stage in a Paul trap, we found serious
limitations in all the calculated waveforms. The important problem of
excluding ions from the Paul trap during the ionization interval has not
previously been adequately investigated. In ICR spectrometry, the ion
exclusion has generally been performed after ionization. The requirements
imposed on such waveforms are less stringent than those that are needed of
waveforms that exclude ions during ionization; in particular, the
frequency content of the waveform must stay uniform throughout the
ionization period because ions are formed throughout the ionization
period. For example, a linear scan (or at least a monotonic scan) of the
resonance ejection frequency is commonly used to exclude ions from an ICR
cell, but such a waveform would not be suitable for ejection during
ionization, because ions created after the frequency has swept past the
resonance frequency would not be ejected.
OBJECTS AND SUMMARY OF THE INVENTION
It is a general object of this invention to provide a method and apparatus
for calculating a time domain waveform to use as an excitation signal for
selectively ejecting ions from a Paul ion trap or an ICR trap mass
spectrometer.
It is another object of this invention to provide a method and apparatus
for providing an ion ejection waveform that is relatively uniform in
frequency content throughout the entire time domain so that ions are
ejected according to their resonant frequency without regard to when in
the time domain they are formed or introduced into the trap.
It is another object of this invention to provide a method and apparatus
for selectively ejecting a range of ions while retaining others.
It is another object of this invention to provide a method and apparatus
for isolating an ion or a selected group of ions in an ion trap.
The foregoing and other objects of the invention are achieved by a method
and apparatus for ejecting unwanted ions formed in or introduced into an
ion trap which traps ions over a predetermined mass range to leave a
higher concentration of wanted ions. Said method and apparatus determines
a plurality of spaced discrete frequencies covering the range of
frequencies of the characteristic motion of unwanted ions and processes
said discrete frequencies to generate a plurality of time dependent
voltage amplitude values which vary throughout the time domain such that
the frequency content of said plurality of time dependent voltage
amplitude values is relatively uniform over the entire time domain, and
such that the magnitude associated with the discrete frequencies is
relatively uniform over the frequency domain.
BRIEF DESCRIPTION OF THE DRAWINGS
Operation of an ion trap to achieve the above and other objects of the
invention will be clearly understood when the following description is
read in conjunction with the accompanying drawings of which:
FIG. 1 is a simplified schematic of a quadrupole ion trap mass spectrometer
along with a block diagram of associated electrical circuits for operating
the mass spectrometer in accordance with the invention.
FIG. 2 shows the time domain calculated by SWIFT (FIG. 2a) from the
magnitude part of the frequency domain shown (FIG. 2b) using a quadratic
variation of the phase part of the frequency domain determined according
to Marshall et al. The Figure was prepared by recording the waveform
created by the apparatus of FIG. 1 using a digital oscilloscope, and
determining the magnitude part of the frequency spectrum by an FFT of the
observed time domain. The observed magnitude spectrum and the observed
time domain are similar in essential aspects to the assigned magnitude
spectrum and the calculated time domain.
FIG. 3 shows a variation on the experiment shown in FIG. 2 in which the
second half of the time domain is removed (FIG. 3a) and in which the first
half of the time domain is removed (FIG. 3b) by electronically gating the
waveform to zero during half of the time domain period.
FIG. 4 shows the result of an experiment in which a waveform of a pure sine
function was calculated assuming a frequency of 175.4 kHz and a clock rate
of 10 MHz (131072 points). The actual clock frequency used to output the
waveform from the arbitrary waveform generator was slowly varied from 9.4
MHz to 10.6 MHz so that the actual frequency spectrum produced by the
waveform also varies.
FIG. 5 shows the same data as FIG. 4, but with the abscissa plotted as the
waveform frequency produced by the waveform; such a presentation is called
here an "ejection efficiency frequency spectrum."
FIG. 6 shows an ejection efficiency frequency spectrum obtained with a
SWIFT waveform calculated according to Marshall with a quadratic variation
of the phase part of the frequency spectrum.
FIG. 7 is an ejection efficiency frequency spectrum obtained with noise
waveforms according to Kelley U.S. Pat. No. 5,134,286.
FIG. 8 is similar to FIG. 7 but differs in the "seed number" that was used
to generate the series of random numbers; this Figure illustrates the
variability that is encountered with different sequences of random
numbers.
FIG. 9 shows the observed time domain of a waveform calculated according to
this invention (FIG. 9a) and the observed magnitude part of the frequency
domain (FIG. 9b). This Figure is intended for comparison with FIG. 2.
FIG. 10 shows a variation on the experiment shown in FIG. 9 in which the
second half of the time domain is removed (FIG. 10a) and the first half of
the time domain is removed (FIG. 10b) by electronically gating the
waveform to zero during half of the time domain period. The frequency
spectra for the two halves of the time domain are essentially the same, in
marked contrast to the similar experiment for the SWIFT waveform (shown in
FIG. 3).
FIG. 11 is an ejection efficiency frequency spectrum obtained with a
waveform calculated according to the invention.
FIG. 12 is another ejection efficiency frequency spectrum obtained with a
waveform calculated according to the invention.
FIG. 13 shows a comparison of part of the mass spectrum obtained with no
waveform being applied during the ionization period (FIG. 13a) and the
mass spectrum obtained by application during the ionization interval of
the waveform of the invention (FIG. 13b). The ionization period in FIG.
13a was 0.6 ms and the abundant ions of m/z 414 and m/z 415 prevented the
storage of ions of m/z 416; the ionization period in FIG. 13b was 25 ms
and the waveform ejected ions of m/z 414 and m/z 415 as they were formed
during ionization so that ions of m/z 416 could be accumulated without
space charge being present.
FIG. 14 shows three ejection efficiency frequency spectra obtained using a
waveform calculated according to the invention. Unlike the ejection
efficiency frequency spectra of the preceding figures, the waveform was
applied during ionization so that ions with a range of m/z values were
present during application of the waveform. FIG. 14a shows a plot of the
total ion abundance after application of the waveform, FIG. 14b shows the
abundance of m/z 131 after application of the waveform, and FIG. 14c shows
the abundance of m/z 132 after application of the waveform.
DESCRIPTION OF PREFERRED EMBODIMENT
There is shown in FIG. 1 at 10 a three-dimensional ion trap which includes
a ring electrode 11 and two end caps 12 and 13 facing each other. A radio
frequency voltage generator 14 is connected to the ring electrode 11 to
supply an r.f. voltage V sin .omega.t (the fundamental voltage) between
the end caps and the ring electrode which provides a substantially
quadrupole field for trapping ions within the ion storage region or volume
16. The field required for trapping is formed by coupling the r.f. voltage
between the ring electrode 11 and the two end-cap electrodes 12 and 13
which are common mode grounded through coupling transformer 32 as shown. A
supplementary r.f. generator 35 is coupled to the end caps 22, 23 to
supply a radio frequency voltage between the end caps; this r.f. generator
produces an arbitrary waveform by sequentially reading a table of
internally stored values and converting them to analog voltages via a
digital-to-analog convertor. The supplementary r.f. generator 35 is
capable of producing different waveforms at different times during the
scan sequence so that, for example, a complex waveform may be produced
during the ionization interval and later in the scan sequence (during the
mass analysis period) a simple sinusoidal waveform may be produced (as
described by Syka et al., U.S. Pat. No. Re. 34,000). The table of stored
values is computed by an external computer and loaded into the digital
memory of the r.f. generator. A filament 17 which is fed by a filament
power supply 18 is disposed which can provide an ionizing electron beam
for ionizing the sample molecules introduced into the ion storage region
16. A cylindrical gate lens 19 is powered by a filament lens controller
21. This lens gates the electron beam on and off as desired. End cap 12
includes an aperture through which the electron beam projects.
Rather than forming the ions by ionizing sample within the trap region 16
with an electron beam, ions can be formed externally of the trap and
injected into the trap by a mechanism similar to that used to inject
electrons. In FIG. 1, therefore, the external source of ions would replace
the filament 17 and ions, instead of electrons, are gated into the trap
volume 16 by the gate lens 19. The appropriate potential and polarity are
used on gate lens 19 in order to focus ions through the aperture in
end-cap 12 and into the trap. The external ionization source can employ,
for example, electron ionization, chemical ionization, cesium ion
desorption, laser desorption, electrospray, thermospray ionization,
particle beam, and any other type of ion source.
The opposite end cap 13 is perforated 23 to allow unstable ions in the
fields of the ion trap to exit and be detected by an electron multiplier
24 which generates an ion signal on line 26. An electrometer 27 converts
the signal on line 26 from current to voltage. The signal is summed and
stored by the unit 28 and processed in unit 29.
Controller 31 is connected to the fundamental r.f. generator 14 to allow
the magnitude and/or frequency of the fundamental r.f. voltage to be
scanned to bring successive ions towards resonance with the supplementary
field applied across the end caps for providing mass selection. The
controller 31 is also connected to the supplementary r.f. generator 35 to
allow the triggering of the arbitrary waveform at the appropriate period
in the scan function. The controller on line 32 is connected to the
filament lens controller 21 to gate into the trap the ionizing electron
beams or an externally formed ion beam only at time periods other than the
scanning interval. Mechanical details of ion traps have been shown, for
example, U.S. Pat. No. 2,939,952 and more recently in U.S. Pat. No.
4,540,884 assigned to the present assignee.
In the SWIFT technique of Marshall et al. (U.S. Pat. No. 4,761,545) the
waveform is computed using the inverse Fourier transform on an assigned
array of phase and magnitude information. The desired frequency array is
readily specified from the known frequency spectrum of ions within the
trap, but the associated phase array is not so readily assigned. The
simplest assignment for the phase array, a constant phase at all
frequencies, yields a waveform from the inverse FT that is essentially a
pulse. In practice, the necessarily limited electronic dynamic range (of
the electronic amplifiers and the digital-to-analog converter) prohibits
adequate physical realization of this type of waveform. Marshall teaches
the use of a non-linear, continuous variation of the phase with frequency,
and he describes the use of a quadratic function in sufficient detail that
one may use the procedure to calculate such a waveform.
As shown by Marshall, such SWIFT waveforms are not pulses, but have an
associated power that is distributed relatively evenly throughout the
waveform. However, such waveforms are essentially frequency scans, as can
be seen by performing a spectral analyses of time windows within the
waveform. For example, FIG. 2 shows the time domain calculated by SWIFT
(FIG. 2a) from the magnitude part of the frequency domain shown (FIG. 2b)
using a quadratic variation of the phase part of the frequency domain
determined according to Marshall et al. This figure was prepared by
recording the waveform created by the apparatus of FIG. 1 using a digital
oscilloscope, and determining the magnitude part of the frequency spectrum
by an FFT of the observed time domain. The observed magnitude spectrum and
the observed time domain are similar in essential aspects to the assigned
magnitude spectrum and the calculated time domain. A spectral analysis of
the first half of the waveform of FIG. 2 is shown in FIG. 3a and a
spectral analysis of the second half of the waveform of FIG. 2 is shown in
FIG. 3b. These spectral analyses of parts of the waveform were
accomplished by electronically gating the waveform to zero, except during
the time window of interest; the frequency spectra were obtained as in
FIG. 2, by recording the waveform with a digital oscilloscope and
performing an FFT on the resulting data. Other spectral analyses of
smaller fractions of the waveform of FIG. 2 show that the time domain
waveform is essentially a frequency scan in which the frequency content is
localized in time and varies systematically during the time course of the
experiment. This is further illustrated by noting the dip in amplitude in
FIG. 2a that appears in the time domain (at about 4 ms) as the frequency
scan reaches the frequency notch at 100 kHz.
Before the introduction of the SWIFT method to ICR spectrometry, ion
ejection was frequently accomplished using electronic hardware that
produced a frequency-swept waveform. Thus to Marshall et al., the
frequency-sweep character of the SWIFT waveforms (calculated with a
quadratic phase variation) was not important because the SWIFT technique
enhanced the existing method: the SWIFT method gives much better control
of the frequency spectrum of the waveform than can be obtained by simply
creating a frequency scanned waveform and creating notches by filtering
the waveform (either digitally or with analog electronics). However, for
experiments in which the waveform is applied during ionization, waveforms
in which the frequency content varies systematically with time are
unsuitable. For example, if the waveform of FIG. 2 were used during
ionization, ions formed at a later time than 4 ms (when the notch appears)
would not experience the notch at all. The characteristic of a systematic
variation in time or a constancy in time of the frequency content of a
waveform will be called here the "temporal spectral homogeneity" of the
waveform. Thus the waveform of FIG. 2 shows poor temporal spectral
homogeneity.
Kelley U.S. Pat. No. 5,134,286 teaches the use of a filtered noise waveform
for excluding ions from the Paul ion trap. We attempted to follow the
method of this inventor, although he did not precisely describe what he
meant by noise, so that his method is not specified as unambiguously as
the method of Marshall et al. We calculated a noise waveform by using a
random number generator with a gaussian distribution, so that the
amplitude of the voltage produced by the system shows a gaussian
distribution. Similarly, waveforms were calculated using a "uniform"
distribution in which the digital value to be converted by the
digital-to-analog convertor was equally likely to be any value within its
range, as contrasted with the gaussian waveforms in which the digital
values are statistically more likely to be closer to zero than to the
extremes of the range. These waveforms were then typically filtered (using
a frequency domain Fourier transform filter) to limit the bandwidth and to
tailor the frequency spectrum to cause the ejection of some ions and
permit the trapping of others.
Spectral analysis of the noise waveforms showed, as anticipated, little or
no systematic variation of the frequency content over the course of the
waveform (good temporal spectral homogeneity), but did show a regrettable
tendency to be uneven in "spectral coverage", wherein certain frequencies
are absent while other frequencies are especially abundant. The smaller
the time window used for the spectral analysis, the more uneven was the
spectral coverage. Thus, in comparison to the SWIFT experiments of FIG. 3
in which the frequency of the waveform varies smoothly with time, the
frequency content of the noise waveform is distributed randomly throughout
the time domain. For small time intervals, a particular frequency may not
be present because of statistical variation. The use of such a waveform
for ion ejection would tend to eject certain ions with good efficiency
while other ions would not be adequately removed because of an unexpected
"hole" in the frequency spectrum. In particular, an ion created late in
the time course of the waveform may or may not be ejected, depending on
the frequency of the ion motion and the vagaries of the frequency spectrum
of the waveform. A higher average power for the entire waveform will tend
to minimize the effect of such holes, but higher power also tends to limit
the resolution of the ion ejection because ions are excited at frequencies
other than their precise resonance frequency, with the effect decreasing
at frequencies farther from the resonance frequency and increasing with
increasing excitation voltage (power).
In practice, when one attempts to exclude undesired ions from the Paul trap
using these noise waveforms, the power level for the entire waveform (the
voltage gain of the amplifier between the digital-to-analog convertor and
the trap electrodes) is adjusted so that ions of masses that are intended
to be trapped do indeed remain trapped, while ions of masses just outside
the mass window are indeed ejected. This results in a power level that is
just sufficient for ion ejection of ions of masses just outside the notch,
but the marginal power level that yields optimum mass ejection resolution
also permits ions to be retained in the trap if their resonance frequency
falls in a hole in the frequency spectrum of the waveform (because of poor
spectral coverage).
Determining whether a waveform shows good spectral coverage is somewhat
more complicated than determining whether a waveform shows good temporal
spectral homogeneity. The latter determination can be readily made by
examining the time course of the frequency spectra for windows of the
waveform as described above, to determine whether the frequency content
varies systematically during the waveform. A preliminary assessment of
spectral coverage may also be made by observing the Fourier transform of
the waveform (or a part of the waveform), but the frequency spectrum may
be misleading about the actual ejection characteristics of a particular
waveform: ions respond to excitation from frequency components other than
that of their precise resonance frequency, and the relative intensities
and phases of these nearby excitations interact in such a complex way that
the ejection efficiency is not obvious from the frequency spectrum.
For this reason an actual measurement of the ejection efficiency gives a
more realistic picture of the spectral coverage. The observation of the
mass spectrum of ions that survive excitation with the waveform is, of
course, one type of measurement of the spectral coverage. However, such a
spectrum is difficult to interpret because it depends on the mass spectrum
of the ions present in the trap before the application of the excitation
waveform, and this mass spectrum may happen to lack ions with resonance
frequencies near features of interest in the frequency spectrum. For the
Paul trap, a more detailed view of the spectral coverage may be obtained
by observing the fraction of ions of a particular m/z value that are not
ejected by the waveform for a series of different r.f. trapping voltages
(which give a particular ion different resonance frequencies). For
example, the following experiment may be performed: ions are created by
electron impact, a particular ion is isolated (by various field
manipulations), the r.f. voltage is adjusted to a particular value, the
waveform is applied between the end electrodes of the trap, and a mass
analysis scan is performed so that the abundance of the ions remaining in
the trap can be determined. A plot of such abundances as a function of the
ion resonance frequency gives the actual ejection efficiency.
An alternate procedure is to use a constant r.f. trapping voltage, but to
adjust the waveform itself. With a digital waveform generator, a "clock"
determines the rate at which points are fetched from memory and converted
to an analog voltage by the digital-to-analog convertor. If a waveform is
calculated assuming some particular clock rate but the waveform is
physically realized using some other clock rate, then all frequencies in
the computed frequency spectrum of the waveform will be present in the
actual waveform at a frequency scaled by the ratio of the real clock rate
to the clock rate used for the calculation. Thus one may perform a series
of experiments in which the r.f. level during ejection remains constant,
but different clock rates are used so that different parts of the computed
frequency spectrum actually effect ejection.
FIG. 4 shows the result of this type of experiment in which a pure sine
function was calculated assuming a frequency of 175.4 kHz and a clock rate
of 10 MHz (131072 points for a duration of 13.1 ms). The r.f. level during
the ejection step of the experiment was chosen so that the resonance
frequency of the ion of interest (m/z 414 from perfluoro-tri-n-butylamine)
was close to 175.4 kHz. All other ions were ejected from the trap before
the waveform was applied (to avoid confusion from space charge effects).
This frequency was chosen to be close to the resonance frequency of this
ion when stored at this r.f. level. This figure is a plot of the abundance
of ions that survive the excitation from the waveform as a function of the
clock rate of the waveform, but the purpose of the experiment is to obtain
information about the waveform itself. Only one ion with one resonance
frequency is ejected from the trap, but one may present the data as the
ejection efficiency as a function of the frequency of the waveform when
created at a clock rate of 10 MHz. For example, when the clock rate is 9.4
MHz, the ion will be responding to the part of the waveform that would
appear at 186.6 kHz in the 10 MHz waveform (10 MHz/9.4 MHz.times.175.4
kHz) and when the clock rate is 10.6 MHz, the ion will be responding to
the part of the waveform that would appear at 165.5 kHz. FIG. 5 is a plot
of the abundance of the ions that survive the excitation waveform as a
function of this "effective waveform frequency". This type of plot will be
called the "ejection efficiency frequency spectrum" of the waveform used
for ejection.
FIG. 6 shows an ejection efficiency frequency spectrum obtained with a
SWIFT waveform calculated according to Marshall (131072 points with a
quadratic variation of the phase spectrum). All frequencies throughout the
range of 165.5 kHz to 186.6 kHz are effective at ejecting ions, and no
extreme variation in the efficiency of ejection is evident(i.e., there is
good spectral coverage). One notable characteristic of this spectrum is
the decrease in abundance as the effective waveform frequency increases.
This is due to a change in the spectral power density as the clock rate
decreases; the same amount of power is compressed into a narrower
bandwidth, and the ions respond to the power level within a band of
frequencies. The general trend in the ejection efficiency spectrum is
therefore more a result of the way the spectrum is acquired than a
characteristic of the waveform. The effect is exaggerated by the selection
of a waveform voltage that is close to the minimum voltage that can cause
ejection, but that is also the voltage that results in maximum ejection
resolution.
FIG. 7 and FIG. 8 are ejection efficiency frequency spectra obtained with
noise waveforms according to Kelley (gaussian noise, 131072 points). The
two waveforms differ in the "seed number" that was used to generate the
series of random numbers, and illustrate the difference that is
encountered with different sequences of random numbers. These spectra
illustrate the poor spectral coverage of noise waveforms. When waveforms
such as these are used to exclude ions from the trap, some ions are
efficiently ejected while others, with resonance frequencies near a hole,
are not ejected at all.
Noise waveforms may also be calculated using the SWIFT technique. The
magnitude part of the frequency spectrum is set to a constant (within the
frequency band of interest, but zero outside of the band) and the phase
part of the frequency spectrum is assigned using random numbers (a
technique commonly called phase randomization). Of course, if the
distribution of the random numbers has a sufficiently small variance, the
resulting time domain waveform will be essentially a pulse, as would be
obtained with a constant phase. However, larger variances produce time
domain waveforms that appear similar to waveforms computed by directly
using random numbers to assign the time domain waveform itself. The
spectral coverage of such SWIFT waveforms is similarly poor and ejection
efficiency frequency spectra obtained using them are qualitatively similar
to FIGS. 7 and 8.
To summarize the necessary characteristics of a waveform used for the
ejection of ions during ionization, the waveform should ideally have a
practically realizable dynamic range, good temporal spectral homogeneity,
and good spectral coverage. The waveforms calculated according to the
methods of the prior art do not meet all three requirements. In
particular, SWIFT waveforms (from a quadratic phase assignment) show good
spectral coverage, but poor spectral homogeneity while noise waveforms
show good spectral homogeneity but poor spectral coverage. Of course, any
possible waveform may be calculated using an inverse FT, but that
theoretical possibility is of little use in actually creating waveforms,
except in those cases where a procedure can be defined for assigning the
phase spectrum.
Two considerations from Fourier theory indicate limits to the achievable
characteristics of digitally produced waveforms. The first is the
well-known Gibb's phenomenon (or Gibb's oscillation) in which a rapid
change in the phase part of the frequency spectrum (a phase discontinuity)
results in a waveform (after the inverse FT) that does not have a true
magnitude frequency spectrum that matches the magnitude frequency spectrum
that was used in the calculation. Thus, as illustrated by Marshall et al.,
if one uses a band of constant amplitude for a magnitude spectrum and a
table of random numbers for the phase spectrum, the frequency spectrum of
the resulting time domain waveform is not a band of constant amplitude,
but rather a band of almost random amplitude. Simply performing the
inverse discrete Fourier transform, followed by the forward Fourier
transform on the same data set will not show the randomness in the
magnitude frequency spectrum. Marshall et al. used zero-filling on the
time domain data set before performing the forward transform. The wildly
varying magnitudes observed in this way are physically real and are not an
artifact of the calculation. To summarize, it is not possible to
simultaneously maintain a constant magnitude frequency spectrum and a
rapidly varying or randomized phase spectrum.
The other consideration from Fourier theory relates to the consequence of a
smoothly varying phase frequency spectrum. Marshall et al. apparently
discovered the usefulness of the quadratic phase function by empirical
means. Later, Guan elegantly showed that this function in fact yields a
time domain waveform of optimally reduced dynamic range (J. Chem. Phys. 91
(2) 775 (1989)). Guan based his argument on the "time-shifting theorem" of
Fourier analysis which states that for a linearly varying phase as a
function of frequency, the wave packet is shifted in the time domain by an
amount proportional to the slope of the linear relation. A constant
magnitude frequency spectrum may be divided into a series of magnitude
frequency spectra, each with an associated phase slope. For a
quadratically varying phase, the slope of the phase varies linearly with
frequency so each of the spectrum parts is linearly shifted in time. This
results in the frequency-sweep character of the total, time domain
waveform. Importantly, by extension any smoothly varying phase function
will lead to poor temporal spectral homogeneity, because of the
association of frequency with time-shifting.
The two considerations from Fourier theory together imply that a waveform
with a true, constant magnitude frequency spectrum cannot also have good
temporal spectral homogeneity. Because of this, we investigated a
different type of waveform, the comb waveform, in which the magnitude
frequency spectrum is a series of discrete peaks, rather than a flat band.
We calculate the comb by summing a series of sine functions of equally
spaced frequency; each point in the waveform is calculated by summing a
series of sines that contains a term for each frequency component in the
desired frequency spectrum. As with the SWIFT waveform, the phase cannot
remain constant because of dynamic range considerations. Our preferred
method of assigning the phase is a quadratic variation with frequency, as
with Marshall's method. The coarseness of the frequency spacing results in
a series of closely spaced peaks in the ejection efficiency spectrum, but
the difference in height between the peaks and the valleys is sufficiently
small that, in practice, there are no holes and ions are ejected with a
relatively uniform efficiency throughout the frequency range. Experience
has shown that in actual practice comb waveforms are effective at
efficiently ejecting all ions with masses within a band, while allowing
reasonably good ejection resolution at the edge of the band or in a notch
in the band.
The specific calculation is as follows:
##EQU1##
where v(t) is the voltage at time t, S.sub.c is a normalization factor (or
gain) to scale the voltage to a value that the system can produce, and
that causes ejection in the desired time interval, n is the number of
discrete frequencies to be added, f.sub.s is the smallest frequency,
f.sub.d is the frequency interval between successive frequencies, p.sub.r
is the "phase rotation factor", and f.sub.0 is the frequency at which the
phase is at a minimum or maximum.
The waveforms used to acquire the ejection efficiency spectra of FIGS. 8
and 9 were typical. The frequencies spanned from 5 kHz to 500 kHz and
f.sub.d was 0.5 kHz. The most critical parameter was the phase rotation
factor (which must be based on the value of f.sub.d). In FIG. 11 the phase
rotation factor was chosen so that
p.sub.r (0.427KHz).sup.2 =2.pi.
That is, the first complete phase rotation at the phase extremum requires a
little less than the interval between the frequencies themselves. If the
phase rotation factor is improperly chosen, the calculated waveform will
show undesirable beats in the time domain so that power is not evenly
distributed at all times. Slight changes in the phase rotation factor may
cause large (and often undesirable) changes in the time domain of the
waveform.
Notches may be entered into a comb-type waveform by either summing two comb
waveforms of non-overlapping frequency content or by omitting from the
calculation of a comb those frequencies that are not to be excited. FIG. 9
shows the observed time domain of a waveform calculated according to the
present invention (FIG. 9a) and the observed magnitude part of the
frequency domain (FIG. 9b). In this case the comb was generated by
omitting a band of frequencies from the calculation. This Figure should be
compared with FIG. 2, in which a SWIFT waveform is shown. Figure 10 shows
a variation on the experiment shown in FIG. 9 in which the second half of
the time domain is removed (FIG. 10a) and in which the first half of the
time domain is removed (FIG. 10b) by electronically gating the waveform to
zero during half of the time domain period. The frequency spectra for the
two halves of the time domain are essentially the same, in contrast to the
corresponding results for a SWIFT waveform shown in FIG. 3. The waveform
of FIG. 9 does not otherwise show the characteristics of a scanned
waveform and therefore shows good temporal spectral homogeneity.
FIGS. 11 and 12 show ejection efficiency frequency spectra obtained with
two similar waveforms calculated according to the present invention. While
the ejection efficiency does vary somewhat with frequency, the variation
is not nearly as pronounced as that obtained with noise waveforms (such as
FIGS. 7 and 8). Also, spectral analysis of small time intervals within the
time domain shows that the frequency content of the waveform does not vary
with the randomness found in noise waveforms. Thus if a waveform such as
that of FIG. 9 were used for ion ejection during the ionization period,
ions formed late in the ionization period would experience an excitation
voltage with much the same frequency content as would ions formed early in
the ionization period. The waveform of the present invention is therefore
superior (for this application) because the frequency content does not
vary systematically as with the SWIFT waveform calculated with a quadratic
phase function and does not vary in the random fashion of the noise
waveforms.
A practical use of a waveform of the type of the present invention is shown
in FIG. 13, in which the accumulation of an ion of interest is made
possible, even though much more abundant ions are present. A mass spectrum
obtained with no waveform being applied during the ionization period (FIG.
13a) is compared to the mass spectrum obtained by application during the
ionization interval of the waveform (FIG. 13b); the ionization period in
FIG. 13a was 0.6 ms and the abundant ions of m/z 414 and m/z 415 (and also
ions of smaller m/z, not shown) prevented storage of the ions of interest,
m/z 416. By using the waveform during ionization, a much longer ionization
period of 25 ms can be used without filling the trap with the abundant
ions of m/z 414 and m/z 415 (and ions of smaller m/z).
Since the spectral coverage for the waveforms of the present invention is
somewhat uneven (as seen in the ejection efficiency frequency spectra of
FIGS. 11 and 12), the ability to discriminate between ions of adjacent m/z
values (and therefore close frequencies) is likely to be inferior to that
shown by SWIFT waveforms, which have been used to separate ions of the
same nominal mass but different exact masses. However, the waveforms of
the present invention can be used to separate ions of a given m/z value
from those of an adjacent m/z value. For example, FIG. 14 shows three
ejection efficiency frequency spectra obtained using a waveform calculated
according to the present invention. Unlike the ejection efficiency
frequency spectra of the preceding figures, the waveform was applied
during ionization so that ions with a range of m/z values were present
during the application of the waveform (as would be the case when the
waveform is used during ionization). FIG. 14a shows a plot of the total
ion abundance after the application of the waveform, FIG. 14b shows the
abundance of m/z 131 after the application of the waveform, and FIG. 14c
shows the abundance of m/z 132 after the application of the waveform.
Clearly, the proper selection of the center frequency of the notch allows
m/z 131 to trapped, while m/z 132 is ejected or allows m/z 132 to be
trapped while m/z 131 is excluded. FIG. 14a, the total ion abundance, has
the appearance of a mass spectrum with unit resolution, which indicates
that the notch itself has a resolution of about 1 m/z unit.
In the calculation of the comb waveform, a critical characteristic is the
difference in frequency between adjacent frequency components (or
"tines"). Since the discrete inverse Fourier transform is calculated as a
sum of equally spaced cosine terms, the comb waveform becomes similar to
the SWIFT waveforms (calculated using a band for the magnitude frequency
spectrum) when the tines are closely spaced. The frequency spacing
produced by the discrete Fourier transform is 1/N.DELTA., where N is the
number of points (in the time domain) and .DELTA. is the sampling interval
and the product N.DELTA. is the duration of the time domain waveform. We
find that the difference in spacing between adjacent frequencies in a comb
waveform should generally be greater than about four times the reciprocal
of the duration of the time domain waveform to achieve adequate temporal
spectral homogeneity, but a frequency spacing of as little as two times
the reciprocal of the duration of the time domain waveform has given
adequate temporal spectral homogeneity in specific applications.
A comb waveform can also be calculated by using the algorithm for the
inverse Fourier transform, by assigning the magnitude frequency spectrum
as properly spaced frequency components (rather than assigning all the
frequencies within the band to be ejected to some constant value, as is
done in the prior art). Another method of performing the calculation is to
generate a comb waveform that covers the entire range of frequencies that
ions may have (so that all ions would be ejected by the application of
this waveform), and then tailoring this waveform to each experiment using
digital or analog filtering techniques.
The tines of the comb need not be evenly spaced. Since the ion m/z values
are spaced at integral values and because of the (approximately) inverse
relationship between the ion resonant frequencies and their m/z values,
the ion resonant frequencies are not evenly spaced. A waveform can be
calculated in which discrete frequencies that correspond to the ion
frequencies are used.
Although the invention has been illustrated and described in connection
with a Paul ion trap, it may apply to analogous structures such as ion
cyclotron resonance instruments, all of which use an ambient magnetic
field. The comb waveform can be applied to the excitation electrodes of
the ion cyclotron resonance cell.
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